Failure of cord-rubber composites by pull-out or transverse fracture

Abstract

A simple theoretical analysis has been developed for the force required to pull out an inextensible cord, or an array of cords, partly embedded in an elastic block. The analysis is based upon Griffith's fracture criterion: that energy supplied by the loading device as the cords are pulled out must be greater than the energy required to fracture the cord-block interface plus any increase in strain energy of the block itself. The pull-out force is obtained in this way as a function of cord diameter, the dimensions of the block, Young's modulus of the block material and the fracture energy per unit area of the interface. Measurements with brass-plated steel wire cords of various diameters, embedded to various depths in rubber blocks of varied dimensions, made of rubber having a wide range of Young's modulus, were all found to be in good agreement with the theoretical predictions. Moreover, the inferred value of the interfacial fracture energy is similar to a directly-measured value for rubber adhering to brass, about 20 kJ m⁻². The theoretical treatment also predicts that the total pull-out force for an array of n cords will increase in proportion to n ^1/2, until transverse fracture intervenes. Both the proportionality to n ^1/2and the predicted transition to transverse fracture instead of cord pull-out have been observed. This broad agreement with the predictions of the theory suggests that the main factors governing cord pull-out have been taken into account.